Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models

Wei min Liu, Simon Asher Levin, Yoh Iwasa

Research output: Contribution to journalArticlepeer-review

660 Scopus citations


When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifurcations, and homoclinic loop bifurcations. These may be important epidemiologically in that they demonstrate the possibility of infection outbreak and collapse, or autonomous periodic coexistence of disease and host. The possible mechanisms leading to nonlinear incidence rates are discussed. Finally, a modified general criterion for supercritical or subcritical Hopf bifurcation of 2-dimensional systems is presented.

Original languageEnglish (US)
Pages (from-to)187-204
Number of pages18
JournalJournal of mathematical biology
Issue number2
StatePublished - Feb 1 1986

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


  • Epidemiology
  • Hopf bifurcation
  • infectious diseases
  • nonlinear incidence rates
  • periodicities


Dive into the research topics of 'Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models'. Together they form a unique fingerprint.

Cite this